Academy Algebra IIAcademy Algebra II

5.9: Write Polynomial Functions 5.9: Write Polynomial Functions

and Modelsand Models

HW: p.397 (4, 6), p.399 (#13)HW: p.397 (4, 6), p.399 (#13)

Write a cubic function whose graph Write a cubic function whose graph passes through the points.passes through the points.

1.) (-4, 0), (0, -6), (1, 0), (3, 0)

Write a cubic function whose graph Write a cubic function whose graph passes through the points.passes through the points.

2.) (-2, 0), (-1, 0), (0, -8), (2, 0)

The table shows the typical speed The table shows the typical speed yy (in feet per (in feet per second) of a space shuttle second) of a space shuttle xx seconds after seconds after

launch. Find a polynomial model for the data. launch. Find a polynomial model for the data. Use the model to predict the time when the Use the model to predict the time when the

shuttle’s speed reaches 4400 feet per second, shuttle’s speed reaches 4400 feet per second, at which point its booster rockets detach.at which point its booster rockets detach.

x 10 20 30 40 50 60 70 80

y 202.4 463.3 748.2 979.3 1186.3 1421.3 1795.4 2283.5

Do Now: Find the x-intercepts Do Now: Find the x-intercepts of the functions.of the functions.

f(x) = 1/6(x + 3)(x – 2)2

Academy Algebra IIAcademy Algebra II

5.8: Analyze Graphs of 5.8: Analyze Graphs of

Polynomial FunctionsPolynomial Functions

HW: p.390 (4-10 even, 16, 20), HW: p.390 (4-10 even, 16, 20),

p.391 (22, 24)p.391 (22, 24)

Turning Points of a GraphTurning Points of a Graph

• The graph of every polynomial function of degree n has at most n – 1 turning points. If the polynomial has n distinct real zeros, then its graph has exactly

n – 1 turning points.• Turning points correspond to a local

maximum or local minimum of the function.

Graph the function. Graph the function. Label the zeros, y-intercepts, and Label the zeros, y-intercepts, and

additional points in-between the zeros.additional points in-between the zeros.• f(x) = 1/6(x + 3)(x – 2)2

Graph the function. Graph the function. Label the zeros, y-intercepts, and Label the zeros, y-intercepts, and

additional points in-between the zeros.additional points in-between the zeros.• f(x) = 4(x + 1)(x + 2)(x – 1)

Use the graphing calculator to graph the Use the graphing calculator to graph the polynomial function. Identify the polynomial function. Identify the

x-intercepts and any local maximum or x-intercepts and any local maximum or minimum points.minimum points.

• f(x) = x4 – 6x3 + 3x2 + 10x – 3

Use the graphing calculator to graph the Use the graphing calculator to graph the polynomial function. Identify the polynomial function. Identify the

x-intercepts and any local maximum or x-intercepts and any local maximum or minimum points.minimum points.

• f(x) = x5 – 4x3 + x2 + 2